In this paper, a new fast algorithm for path planning and a collision prediction framework for two dimensional dynamically changing environments are introduced. The method is called Time Distance (TD) and benefits from the space-time space idea. First, the TD concept is defined as the time interval that must be spent in order for an object to reach another object or a location. Next, TD functions are derived as a function of location, velocity and geometry of objects. To construct the configuration-time space, TD functions in conjunction with another function named "Z-Infinity" are exploited. Finally, an explicit formula for creating the length optimal collision free path is presented. Length optimization in this formula is achieved using a function named "Route Function" which minimizes a cost function. Performance of the path planning algorithm is evaluated in simulations. Comparisons indicate that the algorithm is fast enough and capable to generate length optimal paths as the most effective methods do. Finally, as another usage of the TD functions, a collision prediction framework is presented. This framework consists of an explicit function which is a function of TD functions and calculates the TD of the vehicle with respect to all objects of the environment.

翻译：本文提出了一种适用于二维动态变化环境的快速路径规划新算法与碰撞预测框架。该方法被称为时间距离（TD），其思想源于时空空间概念。首先，将TD概念定义为物体抵达另一物体或某位置所需花费的时间间隔。随后，推导出TD函数作为物体位置、速度与几何形状的函数。为构建构型-时间空间，利用TD函数与另一名为"Z-Infinity"的函数相结合。最后，给出了生成长度最优无碰撞路径的显式公式。该公式中的长度优化通过名为"路由函数"的函数实现，该函数最小化一个代价函数。通过仿真评估了路径规划算法的性能。比较结果表明，该算法具有足够快的速度，且能像最有效的方法一样生成长度最优路径。最后，作为TD函数的另一应用，提出了一种碰撞预测框架。该框架包含一个以TD函数为变量的显式函数，用于计算车辆相对于环境中所有物体的TD值。